A number of estimation techniques can be useful in estimating parameters such as signal frequency, signal repetition rate, rotation angular velocity, frequency-drift, signal modulation classification and the modulation index.
One current technique used in the estimation area is the zero-crossing (or level-crossing) signal repetition test, which is used in frequency estimation, frequency-drift estimation, angular velocity estimation and signal modulation classification. This method takes the average of the time differences between two zero-crossing points of a periodic function. Given N-number of time samples, the existing zero-crossing time estimation technique uses only two zero-crossing time samples for repetition-rate estimation so that it is not robust to random noise and unexpected DC bias in a signal g(x).
The zero-crossing time estimation technique of the prior art is based on a number of important mathematical expressions. Assume in a given time domain xL≦x≦xR, the signal g(x) is periodic and has N number of zero-crossing time samples, or measurements, denoted by x(k), x(k−1), . . . , x(k−N+1), such that g[x(k)]=g[x(k−1)]= . . . =g[x(k−N+1)]=0. The repetition-rate of g(x) in prior art is estimated by the time average:
                                                                        z                ⁡                                  (                  k                  )                                            =                            ⁢                                                2                                      N                    -                    1                                                  ⁢                                                      ∑                                          j                      =                      0                                                              N                      -                      2                                                        ⁢                                                                          ⁢                                                            [                                                                        x                          ⁡                                                      (                                                          k                              -                              j                                                        )                                                                          -                                                  x                          ⁡                                                      (                                                          k                              -                              j                              -                              1                                                        )                                                                                              ]                                        ·                                                                                                                                          =                                ⁢                                  2                  ·                                                                                    x                        ⁡                                                  (                          k                          )                                                                    -                                              x                        ⁡                                                  (                                                      k                            -                            N                            +                            1                                                    )                                                                                                            N                      -                      1                                                                                  ,                                                          (        1        )            By definition, the frequency of g(x) will be:
                                          f            ⁡                          (              k              )                                =                      1                          z              ⁡                              (                k                )                                                    ,                            (        2        )            and the frequency-difference will be:α(k)=f(k)−f(k−1).  (3)Although moving average estimation is used, the prior art estimation relies on only two zero-crossing samples: the first and the last zero-crossing samples for repetition-rate estimation so that it is not robust to random noise, overly sensitive to unexpected DC bias of g(x) and also unreliable.
Thus, there has been a long-felt need for zero-crossing time estimation devices and techniques that do not suffer from the disadvantages, shortcomings and limitations of two-sample estimation, including susceptibility to random noise, sensitivity to unexpected DC bias and lack of reliability. The present inventors have developed a proportional-delayed zero-crossing frequency-drift estimator device that is more robust, reliable and less noisy than the prior art zero-crossing two-sample estimation techniques and does not suffer from the disadvantages, shortcomings and limitations of current estimation techniques.